371 research outputs found
Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals
In this Letter the issue of impulsive Synchronization of a hyperchaotic Lorenz system is developed. We propose an impulsive synchronization scheme of the hyperchaotic Lorenz system including chaotic systems. Some new and sufficient conditions on varying impulsive distances are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived for synchronizing the systems by equal impulsive distances. The boundaries of the stable regions are also estimated. Simulation results show the proposed synchronization method to be effective. (C) 2009 Elsevier Ltd. All rights reserved
Synchronization Based Approach for Estimating All Model Parameters of Chaotic Systems
The problem of dynamic estimation of all parameters of a model representing
chaotic and hyperchaotic systems using information from a scalar measured
output is solved. The variational calculus based method is robust in the
presence of noise, enables online estimation of the parameters and is also able
to rapidly track changes in operating parameters of the experimental system.
The method is demonstrated using the Lorenz, Rossler chaos and hyperchaos
models. Its possible application in decoding communications using chaos is
discussed.Comment: 13 pages, 4 figure
Reduction of dimension for nonlinear dynamical systems
We consider reduction of dimension for nonlinear dynamical systems. We
demonstrate that in some cases, one can reduce a nonlinear system of equations
into a single equation for one of the state variables, and this can be useful
for computing the solution when using a variety of analytical approaches. In
the case where this reduction is possible, we employ differential elimination
to obtain the reduced system. While analytical, the approach is algorithmic,
and is implemented in symbolic software such as {\sc MAPLE} or {\sc SageMath}.
In other cases, the reduction cannot be performed strictly in terms of
differential operators, and one obtains integro-differential operators, which
may still be useful. In either case, one can use the reduced equation to both
approximate solutions for the state variables and perform chaos diagnostics
more efficiently than could be done for the original higher-dimensional system,
as well as to construct Lyapunov functions which help in the large-time study
of the state variables. A number of chaotic and hyperchaotic dynamical systems
are used as examples in order to motivate the approach.Comment: 16 pages, no figure
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